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A chaotic system is one where the outcome is sensitively dependent on initial conditions. Small disturbances can take the system in new, unpredictable directions. Professor Jens Marklof has built a successful career understanding the mathematics that underpin the chaos of quantum systems.

His career, or indeed any academic career, is a kind of chaotic system. You never know which meeting or conversation will send you off in a new direction.

In a fascinating conversation, we explore key moments and opportunities in his career, like introducing himself to Peter Sarnak or sharing an office with David Thouless, shaped the scientist he is today.

Jens was the Rothschild Distinguished Visiting Fellow for the Isaac Newton Institute's programme on Geometric Spectral Theory. His public lecture, "The quantum centenary: from order to chaos" celebrated the 100th anniversary of quantum mechanics.

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This episode was supported by the quantitative research firm G-Research, which has launched a new series of mathematical puzzles called G-Riddles. It's free to try and could win you a cash prize: https://www.gresearch.com/griddles/

Living Proof is the podcast of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.

The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.

Produced by Jon Farrow.

Edited by Keerthi Raj.

Music: 'Origami' by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au

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A father, two of his children, and a family friend — all mathematicians — made progress on a long-standing problem in group theory by coming together at the Isaac Newton Institute.

Listen as Plus Magazine editors Rachel Thomas and Marianne Freiberger interview Roman Sauer, and Uri, Saar, and Shaked Bader to find out more about their research and paths to mathematics.

The Operators, Groups, and Graphs programme was in residence at the INI from July to December 2025: https://www.newton.ac.uk/event/ogg/

The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.

newton.ac.uk

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We talk with Professor Clemency Montelle all about her work decoding the mathematics of ancient manuscripts. In a wide-ranging discussion, we cover some of the concepts that first arose in India, hear about a mentor who hosted meals based on ancient recipes, and learn how important cultural and historical context is for the questions that mathematicians ask.

While she was at the INI, Professor Montelle delivered the Kirk Lecture for the Modern History of Mathematics Programme, which you can watch here: https://www.youtube.com/watch?v=sa2kN-li984

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This episode was supported by the quantitative research firm G-Research, which has launched a new series of mathematical puzzles called G-Riddles. It's free to try and could win you a cash prize: https://www.gresearch.com/griddles/

Living Proof is the podcast of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.

The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.

Produced by Jon Farrow.

Edited by Keerthi Raj.

Music: 'Origami' by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au

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**Correction** At 5:26, the date of the earliest numerical tables is the beginning of the second millenium before the Common Era.

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Imagine if your doctor had a digital model of your heart, personalised to you and updated with your latest medical information. This isn't science fiction – this revolutionary healthcare is being tested now. In this podcast we speak to Steven Niederer, who leads the CVDNet project developing and testing these ideas, and his colleague Richard Wilkinson, from the University of Nottingham.

Richard is one of the organisers of the long research programme, Representing, calibrating & leveraging prediction uncertainty from statistics to machine learning (RCL), held earlier this year at the Isaac Newton Institute for the Mathematical Sciences (INI).

We first spoke to Steven back in 2019 when he helped organise the Fickle Heart programme at the INI. In this podcast, Richard and Steven tell us about digital twins, digital hearts, and how the RCL programme and CVDNet build on the work started back in 2019 with the Fickle Heart programme.

You can find out more about some of the ideas discussed in this podcast in these short introductions:

• Maths in a Minute: Mathematical models
• Maths in a Minute: Differential equations
• Maths in Minute: Machine learning

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In this episode of Living Proof, we speak with Céline and Frank about their book: Why nobody understands quantum physics - and everyone needs to know something about it. They share insights into their writing journey and how each of their backgrounds contributed to the final project.

We met Céline and Frank at the Isaac Newton Institute for Mathematical Sciences in Cambridge, where Frank is co-organising the research programme Quantum field theory with boundaries, impurities, and defects.

"I have learnt that even if you are not a master in mathematics and science you are still able to grasp the essence."

This is Céline Broeckaert talking, believe it or not, about the famously difficult theory of quantum mechanics. Céline knows what she's talking about. She's not a physicist, in fact she's a Romance languages scholar, author and playwright. Yet she's written a book about quantum mechanics together with her physicist husband Frank Verstraete, Leigh Trapnell Professor of Quantum Physics at the University of Cambridge. The book is called Why nobody understands quantum physics - and everyone needs to know something about it. And it's good timing: quantum mechanics celebrates its 100th birthday this year.

See here for an article Plus Magazine published previously about Frank's work.

For a brief introduction to quantum mechanics see A ridiculously short introduction to some very basic quantum mechanics. To find out more about the overlap of maths and art, see here.

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In this episode of the Living Proof podcast we're delighted to meet Moustapha Fall. Moustapha is the Center President of the African Institute for Mathematical Sciences (AIMS) in Senegal and winner of a prestigious Ramanujan Prize for Young Mathematicians from Developing Countries. He also plays an important role on the international stage as Member-at-Large of the Executive Committee of the International Mathematical Union.

Moustapha talks to us about about the amazing institution that is AIMS, about his outreach activities and advice for budding mathematicians, and about the challenges that face mathematicians in sub-Saharan Africa.

You can find the IMU-ICIAM report on fraudulent publishing, which Moustapha mentions in the podcast, here. The same team of authors has also drawn up recommendations on how to fight fraudulent publishing.

We met Moustapha when he visited the Isaac Newton Institute for Mathematical Sciences in Cambridge.

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Earlier this year the the anomalous mathematical patterns sci-art competition attracted some jaw-dropping entries. The competition was held in connection to the Stochastic systems for anomalous diffusion research programme which took place at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge last year.

In this episode of Living Proof, we talk to Codina Cotar, who co-organised the INI programme and helped put on the competition. Codina explains the maths which served as inspiration and discusses some of the winning entries. From coffee to quantum mechanics and from dance to diffusion, find out how mathematics, nature and art are inextricably linked.

Note that the in-person exhibition at the INI is now scheduled for March 2026.

The entries discusses in this podcast are shown below. To find out more about some of the mathematical topics mentioned in this podcast see:

• The Sci-art competition - This article explores some of the mathematics behind the competition, including randomness, diffusion, and many particle systems.
• The Fields Medals 2022: Maryna Viazovska - This article looks at the mathematics of sphere packings, which won a Fields Medal for the mathematician Maryna Viazovska.
• Maths in a Minute: Fluid dynamics - A very bried introduction to the mathematics of liquids and gases.
• A ridiculously short introduction to some very basic quantum mechanics - This article does what the title suggests.
• A brief history of quantum field theory - A deeper look at the theory that arose from quantum mechanics.

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In this episode of Living Proof, we speak with renowned filmmaker Ekaterina Eremenko about her film "Portrait of Olga Ladyzhenskaya", which tells the story of the legendary Russian mathematician celebrated for her groundbreaking work in partial differential equations and fluid dynamics. Ekaterina shares what inspired her to bring Ladyzhenskaya’s life to the screen, explores the creative process behind the film, and reflects on the powerful intersection of art and science.

The film was screened at the Isaac Newton Institute for Mathematical Sciences to celebrate International Women in Mathematics Day 2025.